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2018 Notes on kernels of rational higher derivations in integrally closed domains
Hideo Kojima
Nihonkai Math. J. 29(2): 69-76 (2018).

Abstract

Let $k$ be a field of characteristic $p \geq 0$ and $A = k[x_0, x_1, x_2, \ldots]$ the polynomial ring in countably many variables over $k$. We construct a rational higher $k$-derivation on $A$ whose kernel is not the kernel of any higher $k$-derivation on $A$. This example extends [5, Example 4].

Funding Statement

This work was supported by JSPS KAKENHI Grant Number JP17K05198.

Citation

Download Citation

Hideo Kojima. "Notes on kernels of rational higher derivations in integrally closed domains." Nihonkai Math. J. 29 (2) 69 - 76, 2018.

Information

Received: 24 July 2018; Revised: 4 October 2018; Published: 2018
First available in Project Euclid: 5 August 2019

zbMATH: 07097314
MathSciNet: MR3989233

Subjects:
Primary: 13N10
Secondary: 13F20

Keywords: higher derivation , rational higher derivation , regular field extension

Rights: Copyright © 2018 Niigata University, Department of Mathematics

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Vol.29 • No. 2 • 2018
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